Wednesday, 28 October 2015

quantum mechanics - Separability axiom really necessary?


I know other people asked the same question time before, but I read a few posts and I didn't find a satisfactory answer to the question, probably because it is a foundational problem of quantum mechanics.


I'm talking about the Hilbert space Separability Axiom of quantum mechanics. I'd like to understand why it was assumed this condition in the set of postulates of QFT. Is there a physical motivation of this, or was it only a way to simplify computation?


Mathematically speaking such an assumption is understandable. I read the argument about superselection sectors, where, even in presence of a non separable Hilbert space in QFT, every sector can be assumed to be separable and one can work inside this one, agreeing in this way with the said axiom. But the trouble remain unsolved, why this sector has to be separable?


If you know some old post or some book where I can find this answer and I didn't see please notify me.




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